arXiv:2403.15276 · Nuclear Physics B

Bell-CHSH inequality and unitary operators

M. S. Guimarães, I. Roditi, Silvio Paolo sorella

Published Oct 16, 2024• 6 citations

Abstract

Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The ensuing modifications affecting both classical and quantum bounds are elucidated. The relevance of a particular class of unitary operators whose expectation values are real is pointed out. For these operators, the classical and quantum bounds remain unaltered, being given, respectively, by 2 and 2 2 . As examples, we discuss the explicit realization of phase space Bell-CHSH inequality violation and the Weyl unitary operators for a real scalar field in relativistic Quantum Field Theory.

DOI: 10.1016/j.nuclphysb.2024.116717

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arXiv:2403.15276 · Nuclear Physics B

Bell-CHSH inequality and unitary operators

M. S. Guimarães, I. Roditi, Silvio Paolo sorella

Published Oct 16, 2024• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2024.116717

Related papers

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Abstract Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic quantum field theory. The case of the scalar field in

1+1

1 + 1 Minkowski space-time is scrutinized by relying on the Tomita–Takesaki modular theory. The example of the bounded Hermitian operator

sign(\varphi (f))

s i g n ( φ ( f ) ) , where

\varphi (f)

φ ( f ) stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.

1+1

Minkowski spacetime is scrutinized.

The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum field is revisited by making use of the Hilbert space

{\cal H} \otimes {\cal H}_{AB}

, where

{\cal H}

and

{\cal H}_{AB}

stand, respectively, for the Hilbert space of the scalar field and of a generic bipartite quantum mechanical system. The construction of Hermitian, field-dependent, dichotomic operators is devised as well as the Bell-CHSH inequality. Working out the

AB

part of the inequality, the resulting Bell-CHSH correlation function for the quantum field naturally emerges from unitary Weyl operators. Furthermore, introducing a Jaynes-Cummings type Hamiltonian accounting for the interaction between the scalar field and a pair of qubits, the quantum corrections to the Bell-CHSH inequality in the vacuum state of the scalar field are evaluated till the second order in perturbation theory.

sign(\varphi(f))

, where

\varphi(f)

stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.

\mathcal{H}

and

{\mathcal{H}}_{AB}

AB